# On four-point connectivities in the critical 2d Potts model

### Submission summary

 As Contributors: Sylvain Ribault Arxiv Link: https://arxiv.org/abs/1906.02566v1 Date submitted: 2019-06-25 Submitted by: Ribault, Sylvain Submitted to: SciPost Physics Domain(s): Theor. & Comp. Subject area: High-Energy Physics - Theory

### Abstract

We perform Monte-Carlo computations of four-point cluster connectivities in the critical 2d Potts model, for numbers of states $Q\in (0,4)$ that are not necessarily integer. We compare these connectivities to four-point functions in a CFT that interpolates between D-series minimal models. We find that 3 combinations of the 4 independent connectivities agree with CFT four-point functions, down to the $2$ to $4$ significant digits of our Monte-Carlo computations. However, we argue that the agreement is exact only in the special cases $Q=0, 3, 4$. We conjecture that the Potts model can be analytically continued to a double cover of the half-plane $\{\Re c <13\}$, where $c$ is the central charge of the Virasoro symmetry algebra.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission 1906.02566v1 on 25 June 2019